Variations of permeability and relative permeability due to small-scale heterogeneities, such as cross-bedding, can have a significant impact on reservoir performance1,2 . These properties (particularly relative permeability) are typically very poorly quantified, and yet they represent an important uncertainty in predictions of oil recovery. However, it is currently impossible to model even a single realisation of these small-scale features with a field-scale finite difference simulator.

This paper presents a new, semi-analytical streamline method that allows rapid quantification of this uncertainty. The properties along each streamline are upscaled analytically to provide effective permeability, porosity, relative permeability and geometry for that streamline. This is achieved by a new method for upscaling total mobility in 1dimension, which, combined with an existing method for fractional flow3 , enables us to reproduce production and watercut behaviour versus time for specified rate or pressure well conditions. Production curves from the streamlines are combined numerically to give field-wide values.

A stochastic model of a cross-section through a fluvial reservoir is used to demonstrate that the new method requires only a single pressure solution to calculate the distribution of oil recovery caused by small-scale variations in absolute and relative permeability.

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