Multilateral Well Test Interpretation Model And Numerical Method

Multilateral well technology is one of the cost-effective advanced technologies for oil and gas field development in the modern oil industry. Studies of multi-branch well test analysis technology, to guide the oil and gas development has great significance. However, due to the complexity of the flow mechanism, multi-branch well test analysis technology and theory is not mature enough until now.Based on the summarizes the progress and results of previous studies, according to the flow mechanism of the oil reservoir, Comprehensive using the well test theory, the source function theory, the mathematical physics equations, the numerical methods etc.,this paper focus on three areas of research,which is the study of multi-lateral well test model for dual porous media, method of solving the well test model and method of numerically calculate the analytical solution, through these studies, get the following four main results:(1) established the spherically symmetric point source mathematical model of infinite domains for a dual porosity and anisotropy reservoir, and the point source mathematical model with linear boundary, and the mathematical model with closed or constant pressure or mixed boundary for multi-branch well test mathematical model.(2)By using of the orthogonal transform method,exact solutions for point sources model has been obtained, and through the point source function, the principle of superposition and the mirror reflection principle, the exact solution for three boundary conditions has been obtained, and then the exact solution for multi-branch well model with three boundary conditions has been obtained.(3) By discreting the branch wellbore and time, linear equations composed of the analytical solution of discrete form has been obtained.And then gave the method of using the rectangular numerical integration formula and Gaussian main column elimination for numerical calculation.It solved the inverse problem of the differential equations,when the the amount of fluid is unknown. And automatic fitting method for multi-branch well test is given.(4) Computer program for numerical calculation has been written by vb language, and the results has been plotted into the theoretical charts. Compared with the measured pressure data plates,it proves that the multilateral well test model for dual porosity media and the numerical method for calculating the analytical solution in this paper is correct.