A Natural Variable Fully Implicit Compositional Reservoir Simulation
Bruno Ramon Batista Fernandes1; Kamy Sepehrnoori1; Francisco Marcondes2
1 Center for Petroleum and Geosystems Engineering, The University of Texas at Austin; 2 Federal University of Ceará
doi:10.20906/CPS/CILAMCE2017-0447
Resumo
The fluid flow in porous media, such as oil reservoirs, is described by complex systems of partial differential equations. Several algorithms to solve these equations have been and continue to be proposed in the literature, each having different impact on convergence rate and computational cost for different scenarios. Numerical formulations differ in their nature due to the level of implicitness degree selected, primary variables and primary equations, and solution algorithm. Fully Implicit algorithms are remarkably important due to their stability, which allows the selection of large time-steps, even for complex reservoirs. In this work, a natural variable formulation, in terms of pressure, phase mole fractions, and saturations is presented for the compositional reservoir simulation based on equation of state using Cartesian grids. In the natural variables algorithm, the flow equations are decoupled from the constraint equations (equilibrium relationships) through a Gaussian elimination, significantly reducing the number of variables to be solved in the linear system arising from the discretization of the partial differential equations. The model implemented considers an arbitrary number of components for the flash calculation; up to four-phase flow (aqueous, oleic, gas, and second liquid hydrocarbon phases); no mass transfer between the hydrocarbon phases and the aqueous phase; 3D flow; permeability heterogeneity and anisotropy; advection and dispersion. The natural variable formulation is implemented in the UTCOMPRS Simulator (University of Texas Compositional Reservoir Simulator) and is validated with our original IMPEC (implicit pressure, explicit compositions) formulation and a commercial software for heterogeneous reservoirs. The results are compared in terms of production data, saturation fronts, and computational cost. It is observed that this new formulation is extremely robust, has low computational cost and requires a low number of iterations per time-step.
Palavras-chave: Natural variable; Fully implicit approach; Compositional Reservoir simulation