| In present, finite difference method is the main numerical method of studying the flow in reservoir, meanwhile, finite element method is a valid numerical method and has more superiority than finite difference method, but it is not deeply studied in solving reservoir problems. Some basic and critical problems that appear in the process of applying finite element method to reservoir simulation are studied in this thesis, it lays the foundation for the further research into complex reservoir problems. Topics included in the thesis are as follow:1. Equations of finite element method are established systematically in theory, including single phase flow, oil-water two phases flow, oil-water-gas three phases flow. The types of finite element employed in this thesis are 3-nodes triangle, 4-nodes quadrilateral, 8-nodes hexahedron. Those equations are dispersed in space by using iso-parameter element method and in time by using backward difference method. The linear equations are resolved by variable band Gauss Method, which makes full use of the symmetry and band of stiffness matrix and makes the non-zero element store in one dimension array to reduce occupation in the computer memories.2. To the unstable state flow of single phase fluid, the finite element method is compared with analytical solution, including: planar one-dimension flow, radial flow and three-dimensions flow. The pressure at different position are compared in dimension and dimensionless respectively. It is shown that the finite element solution is precise enough compared to analytical method, which proves that the method and program provided in the thesis are correct, and that it is precise and reliable to solve reservoir problems with the finite element method.3. Some significant factors in finite element analysis, such as time-step, the size of grid and the ratio of grid lengths, are studied and analyzed deeply. It is indicated that those factors are relative and the relative equation is proposed through analysis, which provide valid theoretical rules for finite element analysis.4. The mathmatic model of calculating bottom hole pressure gradient is developed to calculate the pressure gradient in bottom hole reasonably. It can be used to calculate the flow rate precisely , and this is very important in reservoir simulation.5. Simulations are demonstrated in three cases. The first, the production performances of hydrauliclly fractured well are simulatied, meanwhile, the fracture is described carefully and the minimum width of grid describing the fracture in 0.5m only. The geometry of fracture is assumed as rectangle or cuniform, and the transmissibility changes with only distance (having three models ), or changes with only time(having three models ), or changes with distance and time simultaneously(which is a composition about two situation described) , the orientation of fracture is variable. Under the assumption, the well performance is simulated, and different effect is analysed. It is shown that well performance is different when the geometry of fracture and the flow rule in fracture are different. In addition , the influences of fracture length and fracture width andanisotropy of formation to production are studied, the effects of all above factors on well performance are drawn. The assumptions, under which well performance can be simulated precisely , should be that: 1) the geometry of fracture is cuniform, 2) the transmissibility changes with distance and time simultaneously,3) the formation is anisotropy, 4) the fracture have certain orientation angle.The second, the performance of one well group in five-spot pattern is studied. It is shown that the simulation method proposed in this thesis can simulate not only single well performance ,but also well grop performance validly and block performance further.The third, the pressure distribution in mixed boundaries reservoir is studied. It is shown that the finite element method is easy and valid in solving problems with complex mixed boundaries,It provides...
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