Practical implementation of the fractional flow approach to multi-phase flow simulation

Fractional flow formulations of the multi-phase flow equations exhibit seve ral attractive attributes for numerical simulations. The governing equation s are a saturation equation having an advection diffusion form, for which c haracteristic methods are suited, and a global pressure equation whose form is elliptic. The fractional how approach to the governing equations is com pared with other approaches and the implication of equation form for numeri cal methods discussed. The fractional how equations are solved with a modif ied method of characteristics for the saturation equation and a finite elem ent method for the pressure equation. An iterative algorithm for determinat ion of the general boundary conditions is implemented. Comparisons are made with a numerical method based on the two-pressure formulation of the gover ning equations. While the fractional how approach is attractive for model p roblems, the performance of numerical methods based on these equations is r elatively poor when the method is applied to general boundary conditions. W e expect similar difficulties with the fractional flow approach for more ge neral problems involving heterogenous material properties and multiple spat ial dimensions. (C) 1999 Elsevier Science Ltd. All rights reserved.