Decoupled Algorithm with Combined Finite-Element and Finite-Volume Method for Reservoir Simulation

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, other terms and the pressure equation are solved by FEM. The upstream weighted method is adopted to ensure the stability and correctness of calculation when calculating the convective term. To make the calculation easier, the flux of nodes are not calculated node by node as FVM usually do, instead, 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 take advantage of superposition principle, flux of every nods are obtained as load term, then the saturation is solved. 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.