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Petroleum Geoscience

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Influence of fine-scale heterogeneity patterns on the large-scale behaviour of miscible transport in porous media

¹ Department of Irrigation and Hydraulics, Faculty of Engineering, Mansoura University, Mansoura, Egypt (Current address: Hydrology and Ecology Section, Delft University of Technology, PO Box 5048, 2600 GA Delft, Delft, The Netherlands)
² Department of Applied Probability, Faculty of Information Technology and Systems, Delft University of Technology, PO Box 5031, 2600 GA Delft, Delft, The Netherlands
³ Department of Applied Earth Sciences, Faculty of Civil Engineering and Geosciences, Delft University of Technology, PO Box 5028, 2600 GA Delft, Delft, The Netherlands

An extensive series of numerical simulations on two-dimensional flow and miscible transport are carried out. The purpose of performing these simulations is to study the influence of fine-scale heterogeneity patterns (i.e. horizontal laminations, cross-bedding at 45°and 135°) with short range and long range correlation structure on large-scale behaviour of miscible transport in porous media. Synthetic heterogeneous structures have been generated using newly developed stochastic techniques (e.g. the coupled Markov chain method) to model the subsurface formations in various configurations, using realistic characteristics, and the tree-indexed Markov chain method to merge these heterogeneities at various scales. The results of the simulation are compared with simulations on a reference model of heterogeneity where there is no fine-scale heterogeneity. The simulations show that the variation in the fine-scale heterogeneity inside the large-scale lithological units has considerable impact on concentration distribution and the spreading of miscible plumes. The combination of the two stochastic techniques (the coupled Markov chain model and the tree-indexed Markov chain) is a useful tool to study multi-scale transport behaviour in heterogeneous media. The fine-scale heterogeneity enhances the mixing process, but the definition of an asymptotic giga-scopic dispersion at field scale is still questionable.

KEYWORDS: heterogeneity, stochastic process, fluid flow, scale-up, dispersion (flow)