Study on Newton related nonlinear methods in well test analysis, production schedule optimization and reservoir simulation.

摘要

This is a study on the use of alternative nonlinear methods in automated well test analysis, production and injection schedule optimization and in reservoir simulation. In automated well test analysis the advantages and disadvantages of second-order partial derivatives are investigated. Newton's method is shown to be prone to difficulties, however by adjusting the eigenvalues of the Hessian matrix, the performance can be substantially improved. In optimizing the cyclic steam injection process, Newton's method is compared with the Quasi-Newton method using a simplified model to simulate the process. Specific operating strategies for the process are identified. The two methods are then compared in reservoir simulation. Tests show that while it is possible to use the Quasi-Newton method to build up inverse Jacobians as the iterations proceed, for difficult problems the method requires the use of matrix solution techniques. The method then becomes directly comparable to Newton's method. Tests show that depending upon the linear scheme used, and the difficulty of the problem, the Quasi-Newton method may prove to be less expensive than Newton's method in certain cases. The study also addresses the issue of building scalable parallel reservoir simulators. Residual constraints are used to improve the robustness of the parallel matrix solution scheme. The solution of the constraint matrix is shown to be a critical point in achieving good performance on a parallel machine. 60 refs., 47 figs., 18 tabs.