The Theory Research Of Finite Element Method For The Numerical Well Test Analysis

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 theory that appear in the process of applying finite element method to numerical well test analysis are studied in this thesis, it provides the theoretic basis for finite element method studying well test in heterogeneous reservoirs and complex boundary-reservoirs. Topics included in the thesis are as follow:1. Equations of finite element method for single-phase flow in uniform formation and heterogeneous formation are established in theory, the affection of the well bore storage effect and skin effect are considered.2. The method dealing with the internal boundary condition is given in this thesis when well productive in steady prod. rate.3. A numerical simulator is established by Fortran 90, the idea of high modularization and high structuralization are adopted in the program, which has perfect structure and high calculation efficiency, and it is easy to be maintained and be extended.4. To the radial unsteady flow of single-phase fluid in uniform formation and heterogeneous formation, the finite element method is compared with analytical solution, including ignoring well bore storage effect and skin effect and considering these effects. In order to make this research general, the dimensionless quantities are used in comparison. 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 well test problems with the finite element method.5. Some significant factors in finite element analysis, such as the number of elements, the ratio of element lengths and time-step are studied and analyzed deeply. It is indicated that the affection of those factors to precision can not be ignored in numerical well test analysis.6. Simulations are demonstrated for single-phase flow in some typical heterogeneous reservoirs and complex boundary reservoirs. The results are uniform with the theory analysis, it is shown that the method provided in this thesis can be used in studying well test problems in heterogeneous reservoir and complex boundary reservoir.