A number of methods for calculating dynamic pseudo-functions have been developed over the years although there is still a lack of understanding as to why a certain method will succeed in some cases but fail in others. In this paper, we describe the results of an assessment of several methods, namely the Kyte and Berry (KB) method, the Stone method, the Hewett and Archer (HA) method and the Transmissibility-Weighted (TW) method. We have analyzed the equations for deriving the methods and investigated the results of numerical simulations in a variety of cases to enable us to gain new insights into these, and related, upscaling methods.

We start with immiscible gas/oil displacements in horizontal cross-sectional models with 2D → 1D scale-up. For such cases, the potential drop along the system is equal in both phases, i.e. ΔΦo = ΔΦg. Therefore, any method which maintains this equality will be successful. This is the case for the Stone, the HA and the TW methods, but not for the KB method, which uses relative permeability weighting. Despite the fact that the HA and TW pseudos are calculated differently and the shapes of the relative permeability curves are different, the resulting fractional flow curves are identical and hence identical results are obtained in terms of recovery and breakthrough. When the model is dipping, the pressure drops are different in each phase, and the Stone method (which always assumes that ΔΦo = ΔΦg) fails while the HA and TW methods still succeed.

In more complicated models, with 2D → 2D or 3D → 3D scale-up, the fluid mobilities are more important, because they govern the global pressure field and hence the flow paths of the fluids through the system. We show that the HA and TW methods both produce accurate results, provided directional pseudos are used.

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