Petroleum reservoir simulation using super-element method with local detalization of the solution

In this paper, we propose a two-stage method for petroleum reservoir simulation. The method uses two models with different degrees of detailization to describe the hydrodynamic processes of different space-time scales. At the first stage, the global dynamics of the energy state of the deposit and reserves has been modeled (characteristic scale of such changes is km/year). The two-phase flow equations in the model of global dynamics operate with smooth averaged pressure and saturation fields, and they are solved numerically on a large computational grid of super-elements with a characteristic cell size of 200–500 m. The tensor coefficients of the super-element model have been calculated using special procedures of upscaling of absolute and relative phase permeabilities. At the second stage, a local refinement of the super-element model has been constructed for calculating small-scale processes (with a scale of m/day), which take place, for example, during various geological and technical measures aimed at increasing the oil recovery of a reservoir. Then we solve the two-phase flow problem in the selected area of the measure exposure on a detailed three-dimensional grid, which resolves the geological structure of the reservoir, and with a time step sufficient for describing fast-flowing processes. The initial and boundary conditions of the local problem have been formulated on the basis of the super-element solution. To demonstrate the proposed approach, we have provided an example of the two-stage modeling of the development of a layered reservoir with a local refinement of the model during the isolation of a water-saturated high-permeability interlayer. We have shown a good compliance between the locally refined solution of the super-element model.