Verification of a Methodology of Permeability Upscaling using Wavelets

Masoumeh Mofarrah

Research output: ThesisMaster's Thesis

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Fluids in petroleum reservoir flow on a wide variety of physical scales. This behavior is one of the challenging problems, which occurs in modeling and simulation of reservoirs. The geology models, referred to as fine grid models, represent geological variation on very fine scales. Thesis detailed fine models cannot be used directly in numerical simulation. The problem of multiple scales can be solved by using some upscaling or homogenization procedure, in which the reservoir properties are represented by averaged properties and the flow is solved on a coarse grid. In recent years, different upscaling procedures have been developed. Wavelet transformations are one of those methods, which are known as the most efficient method that is being adopted for a vast number of applications such as compression and transformation of data. This master thesis represents the verification of the wavelet transformation in property upscaling of two (2D) and three-dimensional (3D) fine scale geocellular model. In this work, wavelet transformation is applied to scale up the fine property data from “Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques”, which has been published in public domain. The effects of this method on the fine model in terms of the number of blocks, oil in place, pore volume, saving CPU time and memory storage especially in 3D is going to be investigated. In this thesis, behavior of wavelet transformation is studied through upscaling in 2D and 3D. Different coarsening ratios are applied to get coarse models. Then both fine and coarse model are simulated in Petrel with different scenarios to see the flow displacement efficiency of the models. 2D fine scale model has 60 x 220 x 1 cells (13,200 cells), due to size of the model, it is implemented easily in Petrel. The upscaling results are perfectly matched with fine model simulation results. 3D upscaling is applied on two models. Smaller model has 60 x 220 x 20 cells (264,000 cells) and is a sector model of the original SPE 10’s model (85 layers). Properties are scaled up with different coarsening ratios. Observable simulation consequences demonstrate that there is a good match between fine and coarse simulation results. Second model has 60 x 220 x 85 cells (1,122,000 cells) which it is full original SPE 10’s model. Properties are upscaled with a coarsening ratio and simulation results of coarse model are compared with the fine and results presented in the paper. The comparison results show that, there are no significant differences between this study and others.
Translated title of the contributionValidierung einer Upscaling Methode der Permeabilität unter Verwendung von Wavelets
Original languageEnglish
Awarding Institution
  • Montanuniversität
  • Zangl, Georg, Supervisor (external), External person
  • Matthäi, Stephan, Supervisor (internal)
Award date28 Jun 2013
Publication statusPublished - 2013

Bibliographical note

embargoed until null


  • Reservoir
  • Upscaling
  • Wavelet
  • Simulation

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