A Combined Finite-Element and Finite-Volume Method in Reservoir Simulation

摘要

A decoupled algorithm which combines finite-element and finite-volume method (FEM & FVM) for reservoir simulation is presented in the paper. The governing equations of fluid flowing in porous medium are decoupled to solve unknown parameters of pressure and saturation. The convective term of saturation equation is calculated by FVM, while the other terms and the pressure equation are solved by FEM, new method is proposed to make the two methods compatible in one FEM program: the flux are calculated element by element, that is, in each element, local flux of all the nods belong to the element are calculated, then the superposition principle is applied to obtain total flux of every nods as load term, then the saturation can be solved by classic FEM. A water displacing oil problem is calculated based on the method mentioned above. Results show that the method combines the advantages of FEM and FVM, the difficulties of solving saturation with FEM can be consequently solved. Also, the application of decoupled algorithms can greatly reduce storage demands and computational complexity, thus make the simulation more efficiency.