In this paper, we investigate the use of pseudo functions in immiscible two phase displacements in oil-gas systems, where the effects of large mobility differences and gravitational forces are normally encountered. For this specific reason, a new pseudo-isation scheme known as the Transmissibility-Potential-Weighted (TPW) method has been developed and tested against several well-known pseudo methods such as the Kyte and Berry1 , the Stone2 and the Vertical Equilibrium3 (VE) methods. Better performance relative to the other well-known pseudo methods was found especially in the gravity-dominated cases encountered in immiscible gas injection. This is shown for a wide range of cases. In addition, a detailed discussion on the limits and applicability of the VE method is also included.
Based on results from the TPW method, a new grid coarsening scheme for pseudo-isation has been developed and validated. This technique takes into account not only the static properties (i.e. permeability, porosity etc.) of the fine grid models, but also the dynamic properties of the fluid flow. The idea of this coarsening scheme is to identify regions (possibly layers) of the fine grid where there is low variability of gas saturation, and to take such regions as the corresponding coarse grid blocks. The measure of variability used is the coefficient of variation of the gas saturation. The resulting coarsening scheme may be non-uniform, but fulfils the purposes of using pseudo functions (i.e. to control numerical dispersion, to capture the effects of small scale heterogeneity, to reduce the number of grid blocks etc.) with less error and without any adjustment to the pseudo equations themselves.