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The up-scaling of multiphase flow from fine-scale grid data to coarse-scale grid blocks is an important step in the development of numerical models to predict full field behaviour. To perform the up-scaling, use is made of pseudofunctions for fractional flow, relative permeability and capillary pressure. while the use of pseudofunction techniques, such as those proposed by Kyte and Berry, is widespread, the general application of such up-scaled properties generates inconsistent results. This paper proposes that the underlying cause of this discrepancy is the non-constant behaviour of saturation velocities in the original fine-scale simulation.

The concept of length-dependency, or the length-dependent pseudofunction (LDP) method, is introduced in this work to allow coarse grid block models to more closely match the average behaviour of fine-scale models. Using predictions of two-dimensional reservoir displacement with varying amounts of viscous, gravity and capillary interaction, a length-dependent pseudofunction method based upon pseudo fractional flow concepts is compared to results generated through the use of the standard Kyte and Berry method. Results show that in communicating and non-communicating layered models, the proposed length-dependent pseudofunction method provides more accurate estimates of fluid flow behaviour.


In reservoir engineering, the term pseudofunction(s) refer to those properties assigned to a simple model in order that it would produce the important features of the more complex system or reservoir under study. Properties such as pseudo relative permeability and capillary pressure have been employed in reservoir simulation to reduce the number of dimensions of the flow field, hence reducing the number of grid block to a computationally economical number. By using pseudofunction technique, one can replace a finely gridded model based upon laboratory relative permeability and capillary pressure data with a coarser, more homogeneous, system containing effective reservoir properties. These effective, or pseudo, reservoir properties are pseudo relative permeability and capillary pressure functions, or may instead be in the form of a pseudo fractional flow curve.

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