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Institut für Wasserbau - IWS

Selected Topics and International Network Lectures

11:00 Uhr
Dr. Hans Bruining, TU Delft, Faculty of Civil Engineering and Geosciences / Dept. of Geotechnology

Upscaled model, derived from homogenization, for water drive recovery in fractured reservoirs

Zusammenfassung: Homogenization is a powerful method to obtain upscaled equations in situations where a clear separation of scales is possible. The ratio of the small scale with respect to the large scale is denoted by e. The method has been used successfully for a variety of porous media flow problems, e.g. for reactive convection diffusion flows, two phase flow in heterogeneous media, non-Newtonian flow and flow in fractured reservoirs. In this contribution our interest is in water drive recovery from water-wet fractured reservoirs. Our approach follows the ideas of T. Arbogast (TIPM). However, the emphasis in this contribution is on (1) the physical assumptions used in the derivation of the upscaled equation to leading order of e, (2) the use of dynamic constitutive relations (capillary pressures and relative permeabilities) proposed by Barenblatt et al. to obtain the matrix imbibition contribution and (3) the correct implementation of the imbibition contribution in the combined fracture-matrix model. The numerically computed results are compared to the results obtained with the semi-empirical dual-porosity-transfer function method conventionally used by petroleum engineers in their simulators. The advantages of using homogenization for the derivation of transfer functions are discussed.