Pseudofunctions methods have been used to up-scale relative permeability data from the sub-grid scale typical of core data up to grid block sizes used in conventional reservoir simulation. In spite of the widespread use of pseudofunctions, such approaches can be inappropriate due to the use of implicit assumptions regarding the constancy of saturation velocities (as used in the Welge construction).

This work presents an alternative methodology of generating two-phase pseudo relative permeability and capillary pressure functions, using numerical simulation, when non-constant characteristic saturation curves exert a strong impact on the displacement process. The proposed length-dependent pseudofunction technique generates pseudofunctions from 2-dimensional cross-sectional black-oil simulations and later used in a 1-Dimensional reservoir model. The coarse model's simulation predictions are compared to those of the conventional Kyte and Berry method. In addition to this, a case example is given to validate the application of length-dependent pseudos in a 3-dimensional simulation. In this example, sets of length-dependent pseudofunctions were generated and used in a 2-dimensional areal study. Simulation results showed that: a) Curved saturation characteristic velocities occurred in most up-scaled representations and b) The introduction of length-dependent pseudofunctions could result in improved predictions using coarse simulation models.

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