Numerical Simulation Of Compressible Flow In Fractures Using Gas Kinetics Scheme

Compressible flow in fracture widely exists in various industrial and natural processes,such as oil and gas exploration,carbon dioxide storage,and groundwater pollution treatment,etc.It is also a key concern in energy development and environmental protection.For example,near high-pressure gas welbore in nature gas exploitation,the compressibility of gas has significant influence on the flow.In this paper,the compressible flow in fracture is simulated on pore scale using gas kinetic scheme(GKS),and the influencing factors of choked flow are analyzed.The mass flow rate is studied in terms of interporosity flow between matrix rock system and fracture system.The main contents of this study are presented as follows:1.In combination with Cartesian mesh,a gas kinetic scheme is developed for the flow in porous media.The feasibility and effectiveness of the proposed method are verified in simulating incompressible and compressible flow on complex computational domain.The numerical results show that the proposed method can effectively handle complex boundary shapes.Compared with the single-relaxation-time lattice Boltzmann method,the proposed method can precisely implement the no slip boundary condition,thus correctly reflect the characteristics of viscosity-independent permeability.For the complex flow in Berea sandstone slice structure,the simulation results are in good agreement with the experimenta l data,and the permeability can be calculated accurately.2.The compressible flow in a varicose pipe is simulated.A parametric study is carried out to characterize the choked flow in terms of characteristic parameters of the pipe(such as the length of pipe,the amplitude of the bulge,the number of bulges,etc.)and the shape of the cross section.The choking condition is summarized as follows.For varicose pipe,the choking is always occurred at the throat.And the shorter the pipe is or the larger the bulge is or the more bulges exist,the more likely the flow is choked in pipe.The critical pressure ratio has a linear relationship with the length of the pipe.When these parameters are the same,the circular pipe is more likely to choke than the parallel channel.3.A boundary condition of matrix-fracture interporosity flow is proposed,which is related to the average pressure of the gas reservoir,the permeability of the gas reservoir,fracture size and the dynamic viscosity of the gas.And the compressible flow in a circular pipe is studied with the proposed boundary condition.The numerical results show that the total amount of gas flowing into the pipe is a nonlinear function dependent on the ratio of the average pressure of the gas reservoir to the welbore pressure.When the ratio of the average pressure of the gas reservoir to the welbore pressure is large,the mass flow is saturated and the most of the gas in welbore is produced from the lateral boundary of the fracture near the welbore.In summary,this paper combines Cartesian mesh to develop a gas kinetic scheme for the flow in porous media.The feasibility and effectiveness of the proposed method are verified in simulating incompressible and compressible flow on complex computatio na l domain.It provides an effective tool for further study of transport problem in porous media.In addition,a boundary condition of matrix-fracture interporosity flow is proposed,and the influence of interporosity flow around the flow channel near the welbore on compressible flow in the flow channel is analyzed,which lays a foundation for future related research.