With the increasing use of detailed full-field 3D reservoir models, the issue of the correct determination of multiphase flow functions in three directions arises. Reservoir engineers are relatively familiar with the use of kv/kh ratios, but the correct kx/ky/kz functions for multiphase (or even single- phase) flow are less easily estimated. In this paper, we describe a model for a 3D sedimentary structure and we derive directional flow functions using a development of the geopseudo approach.

In order to incorporate the effects of 3D lamina structure, a new method of upscaling has been devised. In this method, the laminae are modelled as a series of plane surfaces. The effective permeability of these planes may be calculated analytically, and then a numerical simulation may be performed to obtain the effective permeability for the whole bed. This method can be used to calculate tensor permeabilities for either single-phase or two-phase flow. In this way we can generate 3D pseudo-functions which may be used as input for larger-scale simulations.

Using both the new method and the traditional Kyte and Berry pseudo-ising approach we have calculated the pseudo relative permeabilities for a model of a fluvial trough crossbed. We show that oil recovery may be significantly influenced by the 3D laminar structure. In particular, the nature of the bounding surfaces of the beds has an important effect on capillary trapping. In beds with high permeability contrast in the laminae, crossflow may be important indicating the need for full tensor upscaling methods.

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