REDUCING ORDER METHODS APPLIED TO RESERVOIR SIMULATION

Resumo

Results obtained by numerical simulations techniques are used in the whole productive life of the reservoir, since exploration until enhanced oil recovery. Numerical simulations involves many cells and heterogeneities and are still limited by the computational time and memory. Reducing Order Methods are a solution to these problems. These methods allow the transformation of high-dimensional models into meaningful representations. It reduces the dimension of the matrices used during the simulations, and consequently, the time and effort. One of the methods used to get a reduced model is the Proper Orthogonal Decomposition (POD). In this work, the mathematical model and equations of a considered reservoir are first presented, and in sequence the discrete system obtained by Finite Difference and Finite Volumes methods. Then, the POD procedure will be described and applied to the problem considered. Finally, the size of new matrices and pressures will be evaluated before and after the reduction, as well as the error involved. The results obtained after the reduction agreed with the physical of the problem and, as expected, the number of unknowns reduced significantly.