| The coupling of porous media flow and free flow is widely present in nature,biomedicine,and industrial fields,such as the coupled flow phenomenon of soil evaporation and the atmosphere,human blood vessel flow and tissue seepage,and fluid flow in fractured-cavity carbonate reservoirs,etc.China’s carbonate reservoirs are rich in reserves and are an important area for increasing reserves and production.Fracture-cavity reservoirs account for two-thirds of the reserves.At present,the research on the coupling of single-phase porous media flow and free flow at home and abroad has become mature,However,in oil reservoirs,there is generally two-phase or even three-phase flow,single-phase flow is not applicable.but the research on the coupling of two-phase porous media flow and free flow is still in its infancy,whether it is from coupling mechanism to theoretical analysis or numerical simulation method is not perfect.In this regard,the main innovations and understandings of this paper are as follows.First,starting from the microscopic pore scale,based on the two-phase flow interfacial tension equation and Navier-Stokes equation,the non-local volume averaging method was applied to carry out the scale upgrade study,and a general volume averaging equation was established.This equation does not introduce any scale constraints,and is applicable in the porous media region,the free flow region and the transition region between the two regions.On this basis,the corresponding REV scale two-phase flow equations are obtained by introducing scale constraints into the porous media and free flow regions respectively.The free flow region is a classic two-fluid model,and the porous media region is a classic two-phase Darcy flow model.Subsequently,the concept of excess physical variables was introduced to derive the mass and momentum transfer equations in the transition region,and then the interface conditions of the two-phase coupled flow were further derived.combined with the above macro two-phase flow equation,a complete mathematical model of two-phase porous media flow and free flow coupling is established.Finally,a macro-scale numerical simulation was carried out based on the established mathematical model.The free flow model was described by the NavierStokes equation,the seepage area was described by the classic Darcy two-phase flow model,and the VOF method was combined with the piecewise linear interface reconstruction method(PLIC)carried out interface tracking,and verified the correctness of the model and numerical method by comparing with microscopic simulation results and experimental results;on this basis,the coupling flow law of different fracture-cavity structure models was summarized and analyzed.The theoretical analysis results show that there are continuity of normal velocity,continuity of normal stress and tangential stress jump on the coupling interface,and the tangent stress jump also manifests as tangential velocity slip.For unfilled karst caves,the numerical model in this paper have better simulation accuracy and accuracy than the traditional Darcy flow model.The traditional Darcy flow model is no longer fully applicable.In the interface tangential direction,the fluid flow in the free flow area is significantly faster than the seepage area,and the fluid in the porous medium area will flow to the free flow area;in the normal direction of the interface,when the fluid is displaced from the porous medium area to the free flow area,At the coupling interface,the two-phase fluid interface will form a liquid film covering the wall,and the oil-water transition zone will narrow.The research methods and results in this paper can provide theoretical basis and technical support for the efficient development of fractured-vuggy carbonate reservoirs. |
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